Angle, Ellwyn, E

Holleman, Euclid C

English

NASA Technical Reports Server

DETERMINATION O F  LONGITUDINAL STABILITY O F  TKE 
B E L L  X-1 AIRPLANE FROM TRANSIENT RESPONSES 
A T  MACH NUMBERS U P  T O  1.12 A T  LJFT 
COEFFICIENTS O F  0.3 AND 0.6 
By Ellwyn E. Angle and Euclid C. Holleman 
Langley Aeronautical Laboratory 
Langley A i r  Farce Base,  Va. 
RESEARCH MEMORANDUM 
+. 
NATIONAL ADVISORY COMMITTEE 
FOR AERONAUTICS 
WASHINGTON 
November 7, 1950 
Declassified September 17, 1958 
A 
https://ntrs.nasa.gov/search.jsp?R=19930086430 2020-06-17T12:29:29+00:00Z
NACA RM L50106a 
NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
RESEARCH MEMORANIXJM 
DETERMINATION OF LONGITUDINAL STABILITY OF THE 
BELL X-1 AIRPLANE FROM TRANSIENT RESPONSES 
AT MACH NUMBERS UP TO 1.12 AT LIFT 
By Ellwyn E. Angle and Euclid C. Holleman 
A number of f ree-f l ight  t ransient  responses resul t ing from small 
s t a b i l i z e r  movements were obtained during f l i g h t  t e s t s  of the  Bel l  
X - 1  airplane (8-percent-thick wing and 6-percent-thick t a i l ) .  Responses 
were analyzed t o  obtain a measure of the longitudinal s t a b i l i t y  charac- 
t e r i s t i c s  of the airplane over the Mach number range from 0.72 t o  1.12 
a t  l i f t  coefficients of 0.3 and 0.6. 
." 
The data presented indicate three s ignif icant  features: (1) The 
darnping varies  great ly  with Mach number, maximum damping occurring a t  
Mach numbers of 0.82 and 1.08 and a minimum damping a t  about 0.93; 
(2) some uncertainty of damping between Mach numbers of 0 . 9 1 t o  0.95 
appears although good agreement with model t e s t s  ex i s t s  throughout the 
Mach number range covered; and (3) the s t a t i c  s t a b i l i t y  of the airplane 
increases with Mach number t o  a Mach number of about 0.93 and decreases 
with fur ther  increasing Mach number. Data above a Mach number of 0.90 
indicate some l i f t -coef f ic ien t  effects .  Agreement of the ful l -scale  
f l i g h t  data and model data over the Mach number range is  good, 
During the course of the f l i g h t  t e s t s  of the Bell X-1 airplane a 
number of airplane responses t o  small s t a b i l i z e r  movements were obtained 
and have been analyzed using the transient-response analysis t o  determine 
the longitudinal-stabili ty derivatives of the airplane. It may be 
pointed out tha t  t e s t s  specif ic  f o r  the application of the transient- 
response analysis were not made, but exis t ing data were selected f o r  
analysis a f t e r  considering conditions such as fixed controls and constant 
Mach number and al t i tude.  
NACA RM L50106a 
Values for  the damping derivatives and the static-stability deriva- 
t ives have been obtained over a range of Mach numbers from O,72 t o  1.12 
a t  l i f t  coefficients of approximately 0,3 and 0.6. 
The data presented are for  the Bell X-1 airplane with an 8-percent- 
thick wing and a 6-percent-thick t a i l .  A more complete investigation 
w i l l  be conducted on the Bell X-1 airplane with a 10-percent-thick wing 
and an 8-percent-thick t a i l  under controlled conditions over as wide a 
range of Mach numbers and l i f t  coefficients as possible. 
SYMBOLS 
forward velocity, feet  per second 
Mach number 
pitching velocity, radians per second 
mass moment of iner t ia  about Y-axis, slug-feet2 
angle of attack, degrees or radians 
ra te  of change of angle of attack, radians per second - 
acceleration due t o  gravity, 32.2 feet  per second per second 
dynamic pressure, pounds per square feet  
mean geometric chord, feet  
mass of airplane, slugs 
wing area, square feet  
horizontal-tail area, square feet  
t a i l  length, fee t  
elevator deflection, degrees, t r a i l ing  edge up i s  negative 
a i r  density, slugs per cubic foot 
normal acceleration, g units 
period of oscillation, seconds 
NACA RM L ~ O I O ~ ~  
H pressure al t i tude,  f ee t  
t time, seconds 
T1/2 time t o  danrp t o  one-half amplitude, seconds 
L l i f t  coefficient (Li f t Iqs)  
CLa r a t e  of change of l i f t  coefficient with angle of a t tack ( a ~ d a a )  
Cm r a t e  of change of pitching-moment coefficient with pitching- Q 
veloci ty  parameter, per  degree 
C ma r a t e  of change of pitching-moment coefficient with angle of attack, per  degree 
it s t a b i l i z e r  incidence, degrees 
"1 amplitude of osc i l la t ion  a t  t = tl 
"2 amplitude of osc i l la t ion  a t  t = t2 .. 
At = t2 - tl 
w natural  frequency of f r ee  osci l la t ion,  radians per  second ( 2 n l ~ )  
C m l h  \ r a t e  of change of pitching-moment coefficient with rate-of-change- 
of-angle-of-attack parameter, per degree 
AIRPLANE AND TEST PROCEIWRJ3S 
Airplane 
A three-view sketch of the Bell  X-1 research airplane (8-percent- 
thick wing and 6-percent-thick t a i l )  i s  presented as figure 1. The 
physical character is t ics  as  used i n  the analysis are  as  follows: 
NACA RM ~ ~ 1 0 6 8  
. . . . . . . . . . . . . . . . . . . . . . . . . . .  m (empty) .  230 
S....e....................e.....o 130 
The moment of i n e r t i a  about the transverse axis was determined 
experimentally f o r  an empty weight condition by osc i l la t ing  the airplane 
as  a single-degree-of-freedom system. An i n e r t i a  correction was estimated 
f o r  various weights corresponding t o  loaded conditions during power-on 
responses. 
A more complete description of the airplane can be found i n  reference 1. 
Instrumentation 
Quanti t ies  measured necessary t o  the determination of the longitudinal- 
s t a b i l i t y  derivatives of the X-1 airplane a re  normal acceleration, a i r -  
speed, altit.ude, pitching velocity, angle of attack, and elevator and 
s t a b i l i z e r  positions. Standard NACA recording instruments were used and 
were synchronized with a common timer. 
- 
Test Procedure 
data presented were analyzed from f l i g h t  t e s t  data obtained 
during climbs t o  maximum a l t i t ude  covering an a l t i t ude  range of 32,000 
t o  64,000 f e e t  and a Mach number range from 0.72 t o  1.12. The t ransient  
osc i l la t ions  analyzed resul ted from a change i n  s t a b i l i z e r  posit ion 
necessary f o r  airplane t r i m  during a l t i t ude  climbs. (The p i l o t  made no 
attempt t o  maintain completely a constant elevator posit ion as woulfl be 
done i n  a specif ic  program for  obtaining t ransient  osci l la t ions.)  I n  
most instances the s t a b i l i z e r  was actuated fo r  a change i n  posit ion of 
approximately lo (not from the same i n i t i a l  posit ion) a t  a r a t e  of 
1.83 degrees per  second. 
Method of Analysis 
I n  dynamic analysis several assumptions must be realized i n  applying 
the various expressions f o r  determining the longitudinal-stabili ty deriv- 
atives.  A two-degree-of-freedom system is assumed involving constant 
values f o r  the forward velocity, a l t i tude,  and control posit ion during 
the t ransient  subsidence which consists of two o r  more complete cycles. 
The expressions f o r  the longitudinal-stabili ty derivatives derived from 
NACA RM ~50106a 5 
a two-degree-of-freedom system similar  t o  the derivatives i n  reference 2 
a re  as  follows: 
C C (sc12 
The term - kt i s  omitted from equation (1) since i t s  
- 
numerical value i s  compared with the frequency term ( 2 x 1 ~ ) ~ .  
The i n i t i a l  s tep i n  the analysis of a given t ransient  osc i l la t ion  
i s  graphical i n  t h a t  the osc i l la t ion  i s  enclosed i n  an envelope formed 
by l ines  connecting the peaks as  shown i n  figure 2. The va l id i ty  of the, 
envelope as  t o  i t s  logarithmic approximation i s  established by p lo t t ing  
the magnitude of the  envelope against time on the semilogarithmic graph 
paper. A s t raight- l ine var iat ion i s  the necessary cr i ter ion.  Once t h i s  
c r i te r ion  i s  sa t i s f ied ,  formulas (1) and (2) may be applied, with necessary 
substi tutions,  t o  determine the airplane longitudinal-stabili ty derivatives. 
ACCURACY 
The accuracy of the data is  indicated by the accuracies of the 
recording instruments as  follows: 
. . . . . . . . . . . . . . . . . . . .  Angle of attack, a, degrees 20.2 
. . . . . . . . . . . .  Pitching velocity, q, radians per  second f0.005 
. . . . . . . . . . . . . . . . . . . . .  Normalacceleration, n, f0.01 
RESULTS AND DISCUSSION 
Transient Responses 
Presented i n  figure 3 are  two representative t ransient  osci l la t ions 
following a small s t ab i l i ze r  disturbance f o r  a high-subsonic Mach n m  
ber (M = 0.82) and a supersonic Mach number (M = 1.02) a t  a l t i tudes  of 
32,000 and 52,000 feet,  respectively. 
The subsonic osc i l la t ion  is  analyzed over the time interval  between 
times 1.0 second and 3.25 seconds. The decay of the pitching-velocity 
t race  over t h i s  time in terva l  is  shown t o  be logarithmic by figure 4. 
It can be seen tha t  once the disturbance ends the elevator i s  maintained 
a t  a reasonably constant value, thus eliminating any appreciable e f fec ts  
of the elevator. The normal-acceleration t race  indicates tha t  the a i r -  
plane -was i n  an approximately level-fl ight condition. 
!The supersonic osc i l la t ion  (f ig .  3) i s  analyzed over the time in terva l  
2.0 t o  4.5 seconds. The decay of the pitching-velocity t race  as t o  i t s  
logarithmic approximation i s  shown i n  figure 4. A s  i n  the high-subsonic 
case, the elevator motion a f t e r  the  i n i t i a l  disturbance ends i s  small, 
eliminating any appreciable elevator e f fec ts  on the oscil lation. 
." 
Longitudinal-Stability Derivatives 
Damping i n  p i tch  Cmq + CmLDa.- The variat ion of the damping-in-pitch 
derivative expressed as Cmq + Cmk with Mach number i s  presented i n  
figure 5. Based on the assumptions made, the damping is  a function of 
the damping derivative Cmq + CmDa a n d  the l i f t -curve slope CL,. The 
l if t-curve slope as  used i n  the reduction of the data t o  the damping 
derivative is  obtained from unpublished full-scale f l i g h t  data and i t s  
variat ion with Mach number i s  presented i n  figure 6. 
This var iat ion of l if t-curve slope was used i n  preference t o  the 
values tha t  could be obtained by p lo t t ing  CL against a f o r  each 
t ransient  response because of a malfunctioning of the angle-of-attack 
indicator during most of the t ransient  responses used. 
Between the Mach numbers 0.72 and 1.12 the damping has s ignif icant  
variations increasing from -0.19 a t  a ~ a c h  number of 0.72 t o  -0.36 a t  a 
Mach number of 0.82, decreasing then t o  a value of -0.14 a t  a Mach num- 
ber of 0.92, and increasing again t o  -0.402 a t  a Mach number of 1.08. 
Minimum damping i s  indicated between the Mach numbers of 0.91 and 0.95. 
Above a Mach number of 1.08 the data indicate decreasing damping with 
increasing Mach number. 
Some uncertainty was encountered i n  the reduction of the data over 
the Mach number range of 0.91 t o  0.95. Presented i n  figure 7 are t i m e  
histories of three transient oscillations i n  th i s  range. Oscillations a 
and b are a t  a Mach number of 0.91 and di f fer  only i n  altitude. Oscilla- 
t ion c begins a t  a Mach number of 0.95 and ends a t  a Mach number of 0.92. 
An attempt has been made t o  analyze these oscillations for  the damping, 
and the values obtained are presented i n  figure 8. Two points above and 
below the Mach number range 0.91 t o  0.95 taken from figure 5 are shown 
t o  indicate the order of magnitude of the variation. 
By examination of the responses i n  figure 7 it can be seen that  the 
oscillations are not entirely free of elevator movement a f t e r  the dis- 
turbance. This could, and probably does, affect the dmqing t o  such an 
extent as t o  make the damping derivatives doubtful even though tbe ele- 
vator effectiveness i s  low. (see reference 3 . )  However, it is nbt pr6b- 
able that  the elevator movement alone could cause such a large change in  
damping as indicated i n  figure 8, but it does provide an argument against 
the use of a simplified transient analysis i n  determining the damping 
derivatives from transient responses with appreciable elevator movement. 
Static-stability derivative .- It has been shown that  the s t a t i c  
s tab i l i ty  of an airplane i s  a function of the natural frequency and the 
rate of decay of the free oscillation. These data obtained from the 
transient oscillations are reduced t o  the variation of airplane s t a t i c  
s tab i l i ty  with Mach number which i s  presented i n  figure 9. Between Mach 
numbers 0.90 and 0.95 there i s  a marked increase i n  Cm, that  is  a 
maximum a t  a Mach number of 0.92. A t  Mach numbers above 0.95 the data 
indicate gradual decreasing s tab i l i ty  t o  a value of -0.034 a t  a Mach 
number of 1.12. 
It should be noted that  several points are calculated neglecting the 
ra te  of decay of the transient oscillation. Since Cro, is for  the most 
part a function of the frequency, these points between the Mach numbers 
0.90 and 0.95 are presented calculated from the frequency only rather 
than being omitted because of the uncertainty of the damping. Between 
Mach number 0.91 and Mach number 1.02 the data indicate an effect of l i f t  
coefficient on the airplane s t a t i c  s tab i l i ty  - lower l i f t  coefficients 
showing lower stabil i ty.  
Comparison of Flight Data and Model Data 
Damping i n  pitch Cm + C 
q rnDae- A comparison of the full-scale 
experimental data estimated from wind-tunnel t es t s  a t  high-subsonic 
speeds (reference 4) and the data obtained from rocket-model t es t s  a t  
supersonic speeds (reference 2) is presented i n  figure 10. It should be 
noted that  the rocket model i s  not of the X-1 airplane but is  of a 
8 NACA RM ~'j0106a 
somewhat similar configuration and is compared ~ L t h  the X-1 scaled t o  
equivalent zt/c i n  figure 11. 
Good agreement exists between the f l ight  data and model data w e r  
the entire Mach number range from 0.72 t o  1.12. It can be seen that  the 
estimated variation of damping between the Mach numbers 0.90 and 0.92 for  
a l i f t  coefficient of approximately 0.3 is  not indicative of any large 
changes i n  damping as characterized by the f l ight  data a t  a lift coef- 
f ic ient  of 0.6. It then appears that  part of the uncertainty of the 
experimental damping may be attributed t o  lift-coefficient effects over 
the Mach number interval from 0.90 t o  0.92 and near the maximum s tab i l i ty  
of the airplane. 
Further investigation i s  t o  be conducted to  determine more completely 
the damping characteristics of the Bell X-1 airplane. 
Static-stability derivative c%* - Presented in figure 12 i s  a com- 
parison of the full-scale experimental data t o  the s tab i l i ty  estimated 
from wind-tunnel data (reference 4) and the free-fal l  data (reference 5) 
a t  high-subsonic speeds. These reference data are corrected t o  a center- 
of-gravity position of 23.2 percent mean aerodynamic chord and pertain 
t o  the airplane with the 10-percent-thick wing. Good agreement exists  
between the full-scale data and the tunnel data t o  a Mach number of 
approximately 0.875 a f te r  which the airplane s tab i l i ty  increases more 
rapidly than is indicated by the tunnel data. The discrepancy between " 
the full-scale data and the free-fall  data may i n  part be due t o  the 
model having a wing thickness of 10 percent as compared t o  a wing thick- 
ness of 8 percent for  the full-scale airplane. Abwe a Mach number of 
0.91 the f l ight  data show good agreement with the free-fall  data for  a 
lift coefficient of about 0.3. 
CONCIXJDING REMARKS 
From the analysis of the transient oscillations of the Bell X-1 a i r -  
plane it was concluded that: 
1. The damping characteristics have significant variations w e r  the 
Mach number interval from 0.72 t o  1.12. The over-all variation is between 
the values -0.19 t o  -0.402 with maximum damping of -0.36 and -0.402 a t  
Mach numbers of 0.82 and 1.08, respectively. Minimum damping i s  indicated 
between the Mach numbers of 0.91 and 0.95. 
2. The damping determined from full-scale f l ight  data is  in good 
agreeme9.t with model data. 
3. Some uncertainty exists as to the changes in damping between 
Mach numbers of 0,91 and 0.95. Damping-derivative values change from 
-1.27 to 0,14 for a Mach number change of 0.91 to 0.95 at a lift coef- 
ficient of 0.6. Comparison of flight data and model data indicates a 
possible lift-coefficient effect. 
4. The airplane static longitudinal stability increases to a n w d m ~ ~ ~  
at a bch number of 0.92 followed by a decrease with further increase in 
Mach number. 
5. The stability determined from flight oscillations is in good 
agreement with model data. 
Langley Aeronautical Laboratory 
National Advisory Committee for Aeronautics 
Langley Air Force Base, Va. 
NACA RM ~50106a 
1. Williams, Walter C., Forsyth, Charles M., and Brown, Beverly P. : 
General Handling-Qualities Results Obtained during Acceptance Flight 
Tests of the Be3.l XS-1 Airplane. NACA RM ~8~09, 1948. 
2. Gillis, Clarence L., Peck, Robert F., and Vitale, A. James: Preliminary 
Results from a Free-Flight Investigation at Transonic and Supersonic 
Speeds of the Longitudinal Stability and Control Characteristics of 
an Airplane Configuration with a Thin Straight Wing of Aspect Ratio 3. 
NACA RM L9K25a9 1950. 
3. Drake, Hubert M., Carden, John R.: Elevator-Stabilizer Effectiveness 
and Trim of the X-1 Airplane to a Mach Number of 1.06, NACA 
RM L50G20, 1950. 
4. Mattson, Axel T., Laving, Donald L.: Force, Static Longitudinal 
Stability, and Control Characteristics of a A - Scale Model of the 16 
Bell XS-1 Transonic Research Airplane at High Mach Numbers. NACA 
RM L8A12, 1948. 
3. Matthews, James T., Jr., and Mathews, Charles W.: Determination by 
the Free-Fall Method of the Longitudinal Stability and Control 
e 
Characteristics of a -Scale Model of the Bell XS-1 Airplane at 4 
Transonic Speeds. NACA RM L8G29aJ 1948. 
NACA RM L>OIOGa 
Figure 1.- Three-view drawing of the Bell X-1 airplane. 
- 
Figure 2,- Graphical approach to analysis of transient responses. 
NACA F34 
~50106a 
NACA RM ~50106a 
Time, t , sec 
Figure 4.- Verification of the constructed envelope of expotential order, 
NACA RM 
~50106~1, 

NACA RM L50106a 
0 
0 / 2 3 
Tm,t,s£c 
.& 
(a) M % 0.91; H = 45,000. 
(b) M z 0.91; H = 55,000. 
Figure 7.- Time histories of transient oscillations between Mach number 0.91 
and 0.95 and lift coefficient of 0.6. 
NACA RM L50106a 
Figure 9.- Variation of static stability with Mach number as determined 
from transient oscillations. 
NACA RM L50106a 
NACA RM L50106a 



Determination of longitudinal stability of the BELL X-1 airplane from transient responses at Mach numbers up to 1.12 at lift coefficients of 0.3 and 0.6

Determination of longitudinal stability of the BELL X-1 airplane from transient responses at Mach numbers up to 1.12 at lift coefficients of 0.3 and 0.6

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